Generation of octave-spanning multiple harmonics for
ultrafast waveform synthesis
The MIT Faculty has made this article openly available. Please share
how this access benefits you. Your story matters.
Citation
Wei-Chun Hsu et al. “Generation of octave-spanning multiple
harmonics for ultrafast waveform synthesis.” Lasers & Electro
Optics & The Pacific Rim Conference on Lasers and ElectroOptics, 2009. CLEO/PACIFIC RIM '09. Conference on. 2009. 12. © Copyright 2010 IEEE
As Published
http://dx.doi.org/10.1109/CLEOPR.2009.5292205
Publisher
Institute of Electrical and Electronics Engineers
Version
Final published version
Accessed
Wed May 25 21:46:28 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/59390
Terms of Use
Article is made available in accordance with the publisher's policy
and may be subject to US copyright law. Please refer to the
publisher's site for terms of use.
Detailed Terms
Generation of Octave-Spanning Multiple
Harmonics for Ultrafast Waveform Synthesis
Wei-Chun Hsu1,2, Zhi-Ming Hsieh1,3, Ying-Yao Lai4, Chien-Jen Lai5, Wei-Ting Chen1, Lung-Han Peng4, Ci-Ling Pan2,
and A. H. Kung1,2
1
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwa n,China
Department of Photonics, National Chiao Tung University, Hsinchu 30010, Taiwan,China
3
Physics Department, National Taiwan University, Taipei 10617, Taiwan,China
4
Institute of Photonics and Optoelectronics, National Taiwan University, Taipei 10617, Taiwan,China
5
Department of EECS, MIT, Cambridge, MA 02139, USA
2
E-mail: sunday2016@gmail.com
Abstract: Up to seven laser harmonics covering more than
two octaves in frequency have been generated efficiently in a
single PPLT crystal, permitting the syntehsis of 1.5
femtosecond pulses in a stable and compact setting.
Keywords: waveform synthesis, quasi-phase-matching
1. INTRODUCTION
Ultrashort subfemtosecond pulses with attosecond timing
are essential for probing the evolution of electronic processes
in atoms and molecules. The ultimate goal of these studies is
to achieve coherent control of electronic motion in matter
with light. To reach this goal it requires developing the ability
to generate light pulses with an octave-spanning spectrum and
having the ability to shape the pulses. There have been two
approaches that can accomplish this. In one approach
single-cycle to sub-cycle pulses are synthesized from a wide
comb of equidistant frequencies generated by adiabatically
driving a Raman coherence with two nanosecond high power
lasers [1].
Another approach produces phase-coherent
optical pulses by phase-locking two femtosecond lasers [2].
An improved version of the latter approach mixes the pulses
from a femtosecond laser with pulses from a
synchronously-pumped OPO to produce a wideband
frequency spectrum [3]. These approaches are all quite
complex and have yet to produce well-controlled and long
lasting waveforms that are needed for applications.
Since the frequency ωq and phase φq of the frequency comb
that Fourier synthesizes to periodic waveforms would satisfy
the conditions:
!q = !ceo + q!m , "q = "0 + q"m
(1)
where ωceo is the carrier-offset frequency, ωm is the comb
frequency spacing, φ0 is a static offset, and φm is a linear
phase difference between adjacent comb components, it is
clear that all the components of the comb are harmonics of
the comb frequency spacing. Thus by starting with a
fundamental frequency at ωm the problem of generating a
wide comb is reduced to that of generating as many
harmonics of ωm as is practical. The solution is simple as
these harmonics can be generated by nonlinear mixing. As
such they naturally will all be phase stable and coherent
relative to each other and could synthesize to long lasting
ultrafast waveforms [4].
In this paper we report the generation of up to seven
phase-coherent harmonics in a single periodically-poled
lithium tantalate crystal. Harmonics 2 to 5 were generated by
efficient quasi-phase-matched (QPM) cascaded sum mixing
from a fundamental wavelength while harmonics 6 and 7
were from random-quasi-phase-matching of the lower
harmonics. These harmonics would produce stable periodic
sub-cycle waveforms in the femtosecond and subfemtosecond
time scale. Note that although multiple harmonics can be
generated using an array of nonlinear crystals, the discrete
arrangement will involve splitting and combining beams and
adjusting beam polarizations several times so that it will lead
to disastrous phase fluctuations and inefficient energy
conversion. Cascaded QPM generation in a single crystal is
compact and efficient. It can be an extremely effective
source for the production of stable ultrafast waveforms.
2. EXPERIMENTAL AND RESULTS
Figure 1 is a schematic depicting the processes used in the
present approach for multiple harmonics generation. For
convenience the fundamental wavelength was chosen at 2406
nm. A nanosecond source at 2406 nm had been constructed
and was available for this experiment. The key component in
this set up is the periodically-poled lithium tantalate (PPLT)
crystal that has been fabricated in house to satisfy sequential
QPM of all four processes inside the crystal. The poled
domain periods in the crystal are 34.09 µm, 22.33 µm, 13.18
Figure 1. Diagram showing scheme of multiple harmonics generation.
Input fundamental wavelength is 2406 nm.
µm,
and
15.90
µm
designed
for
Figure 3. Average power of the harmonics vs input power.
Figure 2. Micrographs of poled domains in the PPLT crystal, showing etched
domains at the boundaries where there is a period change. The corresponding
periods are shown in the inside top of the micrograph.
first order QPM for processes 1-3 and second order QPM for
process 4 at 100 oC respectively for the four processes. Figure
2 shows micrographs of different poled domain regions of the
crystal showing the arrangement of periodic domains at the
transition boundaries.
The PPLT crystal was 2 cm long, 1.3 cm wide and 0.5 mm
thick. The pump beam at 2406 nm was 3.5 ns in duration.
When it was focused through the crystal the input and the
generated harmonics exit the crystal collinearly as a beam of
white light. The beam consisted of primarily the first five
harmonics of the input frequency. The temperature of the
crystal was scanned to optimize the output at the fifth
harmonic of 481 nm. The designed temperature for QPM was
100 oC. Experimentally it was found to occur at 120 oC.
Such a difference is quite common with periodically-poled
crystals mainly because of insufficient refractive index data to
produce a consistent Sellmeier equation for the material.
Figure 3 shows the measured average power at the second
to the fifth harmonic that were monitored as a function of the
input power. At maximum input, corresponding to an
incident intensity of 250 MW/cm2, as much as 30% of the
pump was converted to the higher harmonics. About 25% was
into the second harmonic while the balance 5% was
distributed among the rest. Figure 4 is a picture of the
harmonics taken after they were dispersed by a prism. The
fundamental at 2406 nm cannot be recorded. In addition to
the four recordable harmonics, the sixth and the seventh
harmonics at 401 nm and 344 nm could also be observed. The
strength of these two are quite small as they were generated
only through random phase-matching of the lower harmonics.
3. DISCUSSION
The harmonics thus generated naturally satisfy the
frequency condition of equation (1). By installing a phase
Figure 4. Picture taken with a CCD camera of the images of the second to the
sixth harmonic from the near-ir to the uv dispersed by a prism. The ir and uv
images are those from the phosphorescent sensors.
compensator the phase condition of (1) can also be met.
Consequently it will be possible to Fourier synthesize
waveforms that have stable and controllable carrier-envelope
phases with these outputs. The generated relative intensities
match quite well with those required to synthesize a sawtooth
waveform. Transform-limited pulses synthesized from these
will reach 0.6 cycles with a 500 attosecond field width and
1.4 fs envelope width. In order to reach these durations it will
require modifying the amplitudes of the harmonics.
This cascaded QPM generation and the adiabatic Raman
generation are two techniques that allow full control of the
carrier-envelope phase in waveform synthesis. With the
Raman technique a large number (more than 10) of harmonics
can efficiently be produced in one pass. It is thus most
suitable for generating waveforms with the shortest durations.
The QPM technique we have demonstrated here offers
complementary advantages. It is not locked to a Raman
transition. So the technique can work for any desired input
frequency. It is tunable to the extent allowed by QPM of the
highest harmonic. It requires a rather low input power so that
there is the potential to construct a quasi-CW train of periodic
pulses. The pump duration can be from femtoseconds to the
CW. So this QPM approach offers many new possibilities of
optical waveforms for explorations in ultrafast science and
quantum control.
REFERENCES
[1]
[2]
[3]
[4]
M. Y. Shverdin et al. “Generation of a Single-Cycle Optical Pulse,”
Phys. Rev. Lett. 94, 033904 (2005); Wei-Jan Chen et al.
“Sub-Single-Cycle Optical Pulse Train with Constant Carrier Envelope
Phase,” Phys. Rev. Lett. 100, 163906 (2008).
R. K. Shelton et al. “Phase-Coherent Optical Pulse Synthesis from
Separate Femtosecond Lasers,” Science 293, 1286 (2001).
J. Sun and D. Reid, “Coherent ultrafast pulse synthesis between an
OPO and a laser” Opt. Lett. 34, 854 (2009).
T.W. Hansch, “A proposed subfemtosecond pulse synthesizer using
separate phase-locked laser oscillators,” Opt. Commun. 80, 71-75
(1990).